Are you sure that the mirror is glass? A lot of them are polycarbonate today. If it's polycarbonate or acrylic, you could have crazed the surface trying to get the glue off with acetone. The glue manufacturers make a Remover that doesn't evaporate as quick as acetone. It should be available at hardware stores and home centers.
What's it made of? They found the material that glued barnacles to stuff in the ocean while they were looking for a way to glue parts together after surgery rather than put in stitches. They made the molecule in the lab--it's called ACC and I can't remember all the words or how to spell them right now--and found out how useful it was. They do use the stuff for eye surgery in a purer form.